Using matlab $1\mathrm{.}9$ A storage tank contains a liquid at depth $y,$ where $y=0$ when

the tank is half full. Liquid is withdrawn at a constant flow rate $Q$ to

meet demands. The contents are resupplied at a sinusoidal rate

$3Qsi{n}^2(t).$

FIGURE P $1\mathrm{.}9$

Equation $(1\mathrm{.}13)$ can be written for this system as

$\frac{d(Ay)}{dt}=3Qsi{n}^2(t)-Q$

$([$ change $in$

volume $])=($ inflow $)-($ outflow$)$

or$,$ since the surface area $A$ is constant

$\frac{dy}{dt}=3\frac{Q}{A}si{n}^2(t)-\frac{Q}{A}$

Use Euler's method to solve for the depth $y$ from $t=0$ to $10d$ with

a step size of $0\mathrm{.}5d.$ The parameter values are $A=1250m^2$ and

$Q=450\frac{m^3}{d}.$ Assume that the initial condition is $y=0.$